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In facsimiwe and (anawog) tewevisiontransmission, muwtipaf causes jitter and ghosting, seen as a faded dupwicate image to de right of de main image. Ghosts occur when transmissions bounce off a mountain or oder warge object, whiwe awso arriving at de antenna by a shorter, direct route, wif de receiver picking up two signaws separated by a deway.

Radar muwtipaf echoes from an actuaw target cause ghosts to appear.

In radar processing, muwtipaf causes ghost targets to appear, deceiving de radar receiver. These ghosts are particuwarwy bodersome since dey move and behave wike de normaw targets (which dey echo), and so de receiver has difficuwty in isowating de correct target echo. These probwems can be minimized by incorporating a ground map of de radar's surroundings and ewiminating aww echoes which appear to originate bewow de ground or above a certain height (awtitude).

In a Gwobaw Positioning System receiver, Muwtipaf Effect can cause a stationary receiver's output to indicate as if it were randomwy jumping about or creeping. When de unit is moving de jumping or creeping may be hidden, but it stiww degrades de dispwayed accuracy of wocation and speed.

At de receiver, due to de presence of de muwtipwe ewectromagnetic pads, more dan one puwse wiww be received, and each one of dem wiww arrive at different times. In fact, since de ewectromagnetic signaws travew at de speed of wight, and since every paf has a geometricaw wengf possibwy different from dat of de oder ones, dere are different air travewwing times (consider dat, in free space, de wight takes 3 μs to cross a 1 km span). Thus, de received signaw wiww be expressed by

where N{\dispwaystywe N} is de number of received impuwses (eqwivawent to de number of ewectromagnetic pads, and possibwy very warge), τn{\dispwaystywe \tau _{n}} is de time deway of de generic nth{\dispwaystywe n^{f}} impuwse, and ρnejϕn{\dispwaystywe \rho _{n}e^{j\phi _{n}}} represent de compwex ampwitude (i.e., magnitude and phase) of de generic received puwse. As a conseqwence, y(t){\dispwaystywe y(t)} awso represents de impuwse response function h(t){\dispwaystywe h(t)} of de eqwivawent muwtipaf modew.

More in generaw, in presence of time variation of de geometricaw refwection conditions, dis impuwse response is time varying, and as such we have

τn=τn(t){\dispwaystywe \tau _{n}=\tau _{n}(t)}

ρn=ρn(t){\dispwaystywe \rho _{n}=\rho _{n}(t)}

ϕn=ϕn(t){\dispwaystywe \phi _{n}=\phi _{n}(t)}

Very often, just one parameter is used to denote de severity of muwtipaf conditions: it is cawwed de muwtipaf time, TM{\dispwaystywe T_{M}}, and it is defined as de time deway existing between de first and de wast received impuwses

In practicaw conditions and measurement, de muwtipaf time is computed by considering as wast impuwse de first one which awwows receiving a determined amount of de totaw transmitted power (scawed by de atmospheric and propagation wosses), e.g. 99%.

Keeping our aim at winear, time invariant systems, we can awso characterize de muwtipaf phenomenon by de channew transfer function H(f){\dispwaystywe H(f)}, which is defined as de continuous time Fourier transform of de impuwse response h(t){\dispwaystywe h(t)}

where de wast right-hand term of de previous eqwation is easiwy obtained by remembering dat de Fourier transform of a Dirac puwse is a compwex exponentiaw function, an eigenfunction of every winear system.

The obtained channew transfer characteristic has a typicaw appearance of a seqwence of peaks and vawweys (awso cawwed notches); it can be shown dat, on average, de distance (in Hz) between two consecutive vawweys (or two consecutive peaks), is roughwy inversewy proportionaw to de muwtipaf time. The so-cawwed coherence bandwidf is dus defined as

BC≈1TM{\dispwaystywe B_{C}\approx {\frac {1}{T_{M}}}}

For exampwe, wif a muwtipaf time of 3 μs (corresponding to a 1 km of added on-air travew for de wast received impuwse), dere is a coherence bandwidf of about 330 kHz.